With 128 heads of state or government having gathered in one place (a record, according to the United Nations), they broke into smaller groups throughout the day for sometimes contentious meetings in which these world leaders themselves did the tough word-for-word haggling over texts that is usually handled by aides.

It was more global than any international debate in history, at least in the sense that it was the first among so many world leaders that concerned the bedrock habitability -- for humans and many other species -- of the only home we've got.

This debate was within what is at times called The Family of Man.

At the moment, it appears that Mother Earth and Mother Nature are at the head of the table.

And as President Obama quoted at some point months ago, "If Mama ain't happy, ain't nobody happy."

But some eminent American climate scientists are greatly encouraged by the high-level arguments that took place -- often simply because they did.

Central among these day-long wranglings were a meeting between the leaders of China, the United States, India, Brazil and South Africa, as well as other meetings involving those five and some 25 other leaders.

"I have never seen anything like it," U.N. Secretary General Ban Ki Moon told ABC News 36 hours later on a plane flying back to New York. "It makes a big difference when the top leaders talk to each other."

Obama to Hillary Clinton During Climate Talks: 'I'm Losing Patience'

At one point at a bargaining table, as one participant who was in the room told ABC News, Obama leaned over to Secretary of State Hillary Clinton, sitting to his left, and said, only somewhat sotto voce, "I'm trying to be constructive here, but I'm losing patience."

At another point, as The Washington Post reported, "After Obama asked whether the Chinese could commit to listing their climate targets in an international registry, Xie Zhenua ... China's top climate negotiator [who had already] exploded in rage at U.S. pressure ... launched into a tirade, pointing his finger at the U.S. president."

But then a remarkable thing happened.

China's Premier Wen Jiabao, reported to be "passionate" about the urgent need for action on global warming, instructed the translator not to translate what Xie had said.

Perhaps Xie's tone and body language made any translation unnecessary.

Nor does it seem probable that the Americans or their friends in the room would not have included someone who understood Chinese.

It wasn't too long after that, as an official who was in the room told ABC News, that Wen "suddenly offered a slight change of tone that made things possible" and suggested that there could, after all, be a sort of language on the vexed "transparency" issue that China might live with.

"A little window," said this official, holding his hand up with the tips of his thumb and index finger barely an inch apart, "but enough."

Soon after that, the official said, President Obama was talking to the cameras, then heading for the airport, hours behind schedule, and wheels up in hopes of beating the record snowstorm barreling down on Washington.

(Ironically, it was just the sort of "very heavy precipitation," whether rain or snow, long predicted by scientists to increase in frequency in the upper eastern and northeastern United States as a result of human-induced global warming, and which, over the past 30 years, has in fact materialized there. This can be seen on pp. 32 and 44, inter alia, in the US government's recent report, approved by 13 federal agencies, "Global Climate Change Impacts in the U.S.," which can be found by clicking here.)

Climate Change Train 'Finally Leaving the Station'

Yohe, a member of the IPCC team that shared the Nobel Peace Prize in 2007, has long been a leading authority in the now fast-growing field of environmental economics

He said his life's work has essentially been about trying to help humanity get a handle on global warming.

"After what happened in Copenhagen on that Friday, and what Obama did -- risking himself like that -- I woke up on Saturday and just knew ... the train was finally leaving the station," Yohe said.

"How to get the train out of the station" is a phrase economists and policy makers have used for years when talking about the task of getting American and other major governments to make the big adjustments necessary to respond to dangerous global warming in a coordinated effort to cut emissions and reassign dollars to help people around the world deal with the warming that cannot be avoided.

'America Now Part of the Solution' on Global Warming, Economist Says

"What I really loved was that the U.S. was now part of the solution, not part of the problem," Yohe said of his Saturday morning realizations.

He added that it might now appear to many people that China was still "part of the problem."

China has been widely reported to have stubbornly, and at times even fiercely, resisted requests by other countries at the summit to compromise on matters of transparency about their emissions policies, and on other matters.

"The Chinese fought tooth and nail," against unambiguous language about considering 1.5 degrees Celsius (above pre-industrial temperatures) according to another official who had been in the room and who also requested anonymity.

Why, we asked.

"One reason," this official told ABCNews, "is that the Chinese have done their own climate studies and concluded that they cannot do better than 2 degrees Celsius above pre-industrial levels."

Yohe, on hearing of this, told ABC, "And, to spin that another way -- you've got to give credit to the Chinese, perhaps, for not wanting to promise something they don't think they can deliver."

Yohe's tears of happiness were matched by the beaming smile on the face of Columbia University agronomist Cynthia Rosenzweig at the baggage carrousel after the plane from Copenhagen had landed back in the United States.

Recognizing this reporter, for whom she had previously done an interview on the affects of global warming, Rosenzweig came up and said, "Isn't it great? I may be in a minority, but I feel.... Here we go! It's been exactly 25 years since I published my first paper on how global warming was going to alter wheat production in north America."

"Now we can get to work!" she said. "All the big parties have engaged."

'A Pretty Happy Camper'

"The talks didn't fail. ... I'm going away from COP 15 [the climate summit] a pretty happy camper," University of Texas at Austin ecologist Camille Parmesan wrote in an informal email to some friends and journalists.

Parmesan is widely respected for her work on assessing the impacts of human-induced global warming on ecosystems around the world.

"I didn't expect a treaty from this -- don't know why anyone would have. Isn't this the first time in many years that both the USA and China are here to seriously participate?" Parmesan wrote. "What I had hoped was that serious talks could begin, and that there would be a general feeling that agreement on details could be reached over the next years, and pretty much that's what happened."

"I was thrilled to hear that Obama had a one-on-one with the Chinese Premier," she wrote. "We can't have global agreement on such an important and highly charged issue until the Heads themselves can sit face to face and talk frankly... It's the true beginning of the road to a treaty."

Plenty of Reality Checks

While some leading American climate scientists clearly now feel elation after so many years trying to warn the world about the dangers of unchecked climate change, these hopes are nonetheless counterbalanced by plenty of awareness -- and more worried warnings from other scientists -- about the inadequacies of the Copenhagen Accord, to say nothing of the fact that it is entirely non-binding, and was, officially, simply "noted" by the Conference of the Parties to the U.N. Framework Convention on Climate Change.

Leading climatologist Richard Somerville, professor emeritus at Scripps Institution of Oceanography in San Diego, told ABC News that "Mother Nature imposes a timescale on when emissions need to peak and then begin to decline" if highly dangerous warming is to be avoided.

"This urgency is not ideological or political, but rather is due to the physics and biogeochemistry of the climate system itself," he said.

Somerville and 25 other leading scientists from eight countries published the report, which can be found here, just before the Copenhagen summit as an update, based on more than 200 peer-reviewed studies, to the science on the most recent report of the U.N.'s Intergovernmental Panel on Climate Change, which is now three years old and outmoded in some important ways, especially regarding the acceleration of sea level rise.

This graph depicts three different scenarios for drastic emissions cuts that must be taken worldwide if the average global temperature is to be kept below 2 degrees Celsius above pre-industrial averages.

"Even if everything promised in the new Copenhagen Accord were successfully executed, it would still cap the temperature rise at about 3 degrees, at best, not 2," he said.